Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

TL;DR

This paper constructs simple solutions within IKKT-type matrix models that describe quantum cosmological space-times with a regular Big Bang, featuring a signature change and no target space singularities.

Contribution

It introduces novel matrix model solutions representing homogeneous, isotropic cosmologies with a resolved Big Bang via signature change in a fuzzy brane framework.

Findings

The models exhibit a regular Big Bang with a signature change.

Solutions include both recollapsing and expanding universes.

The Hubble parameter is singular at the Big Bang but diminishes at late times.

Abstract

We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.